// NOTE: compile with g++ filename.cpp -std=c++11

#include <iostream>
#include <cmath>
#include <cstdlib>
#include <algorithm>
#define DIM 1024
#define DM1 (DIM-1)
#define _sq(x) ((x)*(x)) // square
#define _cb(x) abs((x)*(x)*(x)) // absolute value of cube
#define _cr(x) (unsigned char)(pow((x),1.0/3.0)) // cube root

unsigned char GR(int,int);
unsigned char BL(int,int);

unsigned char RD(int i,int j){
double a=0,b=0,c,d,n=0;
while((c=a*a)+(d=b*b)<4&&n++<880)
{b=2*a*b+j*8e-9-.645411;a=c-d+i*8e-9+.356888;}
return 255*pow((n-80)/800,3.);
}

unsigned char GR(int i,int j){
double a=0,b=0,c,d,n=0;
while((c=a*a)+(d=b*b)<4&&n++<880)
{b=2*a*b+j*8e-9-.645411;a=c-d+i*8e-9+.356888;}
return 255*pow((n-80)/800,.7);
}

unsigned char BL(int i,int j){
double a=0,b=0,c,d,n=0;
while((c=a*a)+(d=b*b)<4&&n++<880)
{b=2*a*b+j*8e-9-.645411;a=c-d+i*8e-9+.356888;}
return 255*pow((n-80)/800,.5);
}

void pixel_write(int,int);
FILE *fp;
int main(){
    fp = fopen("MathPic.ppm","wb");
    fprintf(fp, "P6\n%d %d\n255\n", DIM, DIM);
    for(int j=0;j<DIM;j++)
        for(int i=0;i<DIM;i++)
            pixel_write(i,j);
    fclose(fp);
    system("ffmpeg -i MathPic.ppm MathPic.bmp");
    system("MathPic.bmp");
    return 0;
}
void pixel_write(int i, int j){
    static unsigned char color[3];
    color[0] = RD(i,j)&255;
    color[1] = GR(i,j)&255;
    color[2] = BL(i,j)&255;
    fwrite(color, 1, 3, fp);
}